Geographic Gossip: Efficient Averaging for Sensor Networks

TL;DR

This paper introduces a geographic gossip algorithm that significantly improves the efficiency of distributed averaging in sensor networks by leveraging geographic routing, outperforming standard gossip protocols especially on grid and random geometric graph topologies.

Contribution

The paper presents a novel geographic gossip scheme that exploits geographic information to enhance averaging efficiency in sensor networks, reducing communication costs compared to traditional methods.

Findings

Improves averaging efficiency by factors of n and √n on regular graphs.

Achieves O(n^{1.5}/√log n) transmissions on random geometric graphs.

Demonstrates substantial theoretical and experimental performance gains over standard gossip algorithms.

Abstract

Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste in energy by repeatedly recirculating redundant information. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is related to the slow mixing times of random walks on the communication graph. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing geographic routing combined with a simple resampling method, we demonstrate substantial gains over previously proposed gossip protocols. For regular graphs such as the ring or grid, our algorithm improves standard gossip by factors of $n$ and $\sqrt{n}$ respectively. For the more challenging case of random geometric graphs, our algorithm computes the true average to accuracy $\epsilon$ using $O(\frac{n^{1.5}}{\sqrt{\log n}} \log \epsilon^{-1})$ radio transmissions, which yields a $\sqrt{\frac{n}{\log n}}$ factor improvement over standard gossip algorithms. We illustrate these theoretical results with experimental comparisons between our algorithm and standard methods as applied to various classes of random fields.